vegan (version 2.7-2)

mantel: Mantel and Partial Mantel Tests for Dissimilarity Matrices

Description

Function mantel finds the Mantel statistic as a matrix correlation between two dissimilarity matrices, and function mantel.partial finds the partial Mantel statistic as the partial matrix correlation between three dissimilarity matrices. The significance of the statistic is evaluated by permuting rows and columns of the first dissimilarity matrix. Test is one-sided and only tests that distances are positively correlated.

Usage

mantel(xdis, ydis, method="pearson", permutations=999, strata = NULL,
    na.rm = FALSE, parallel = getOption("mc.cores"))
mantel.partial(xdis, ydis, zdis, method = "pearson", permutations = 999, 
    strata = NULL, na.rm = FALSE, parallel = getOption("mc.cores"))
# S3 method for mantel
summary(object, ...)

Value

The function returns a list of class mantel with following components:

Call

Function call.

method

Correlation method used, as returned by cor.test.

statistic

The Mantel statistic.

signif

Empirical significance level from permutations.

perm

A vector of permuted values. The distribution of permuted values can be inspected with permustats function.

permutations

Number of permutations.

control

A list of control values for the permutations as returned by the function how.

Details

Mantel statistic is simply a correlation between entries of two dissimilarity matrices (some use cross products, but these are linearly related). However, the significance cannot be directly assessed, because there are \(N(N-1)/2\) entries for just \(N\) observations. Mantel developed asymptotic test, but here we use permutations of \(N\) rows and columns of dissimilarity matrix. Only the first matrix (xdist) will be permuted, and the second is kept constant. See permutations for additional details on permutation tests in Vegan.

Partial Mantel statistic uses partial correlation conditioned on the third matrix. Only the first matrix is permuted so that the correlation structure between second and first matrices is kept constant. Although mantel.partial silently accepts other methods than "pearson", partial correlations will probably be wrong with other methods.

Borcard & Legendre (2012) warn against using partial Mantel test and recommend instead Mantel correlogram (mantel.correlog).

The function uses cor, which should accept alternatives pearson for product moment correlations and spearman or kendall for rank correlations.

References

Borcard, D. & Legendre, P. (2012) Is the Mantel correlogram powerful enough to be useful in ecological analysis? A simulation study. Ecology 93: 1473-1481.

Legendre, P. and Legendre, L. (2012) Numerical Ecology. 3rd English Edition. Elsevier.

See Also

mantel.correlog.

Examples

## Is vegetation related to environment?
data(varespec)
data(varechem)
veg.dist <- vegdist(varespec) # Bray-Curtis
env.dist <- vegdist(scale(varechem), "euclid")
mantel(veg.dist, env.dist)
mantel(veg.dist, env.dist, method="spear")